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Simulating open quantum systems is key to understanding non-equilibrium processes, as persistent influence from the environment induces dissipation and can give rise to steady-state phase transitions. A common strategy is to embed the…
We model a situation in which a collection of species derive their fitnesses via a rock-paper-scissors-type game; however, the precise payoffs are a function of the environment. The new aspect of our model lies in adding a feedback loop:…
Eco-evolutionary dynamics is crucial to understand how individuals' behaviors and the surrounding environment interplay with each other. Typically, it is assumed that individuals update their behaviors via linear imitation function, i.e.,…
Spin chains with open boundaries, such as the transverse field Ising model, can display coherence times for edge spins that diverge with the system size as a consequence of almost conserved operators, the so-called strong zero modes. Here,…
A classical approach for the analysis of the longtime behavior of Markov processes is to consider suitable Lyapunov functionals like the variance or more generally $\Phi$-entropies. Via purely analytic arguments it can be shown that these…
Conserved dynamical systems are generally considered to be critical. We study a class of critical routing models, equivalent to random maps, which can be solved rigorously in the thermodynamic limit. The information flow is conserved for…
In evolutionary game theory, repeated two-player games are used to study strategy evolution in a population under natural selection. As the evolution greatly depends on the interaction structure, there has been growing interests in studying…
Recent theories from complexity science argue that complex dynamics are ubiquitous in social and economic systems. These claims emerge from the analysis of individually simple agents whose collective behavior is surprisingly complicated.…
Real-world data streams naturally include the repetition of previous concepts. From a Continual Learning (CL) perspective, repetition is a property of the environment and, unlike replay, cannot be controlled by the agent. Nowadays, the…
Evolutionary dynamics provides an iconic relationship --- the periodic frequency of a game is determined by the payoff matrix of the game. This paper reports the first experimental evidence to demonstrate this relationship. Evidence comes…
Recurrent boom-and-bust cycles are a salient feature of economic and financial history. Cycles found in the data are stochastic, often highly persistent, and span substantial fractions of the sample size. We refer to such cycles as "long".…
We consider synchronous iterative voting, where voters are given the opportunity to strategically choose their ballots depending on the outcome deduced from the previous collective choices.We propose two settings for synchronous iterative…
We elucidate the role that the dissipation in a bosonic channel plays in the prevalence and stability of time crystals (TCs) in a periodically driven spin-boson system described by the Dicke model. Here, the bosons are represented by…
The stability of linear dynamic systems with hysteresis in feedback is considered. While the absolute stability for memoryless nonlinearities (known as Lure's problem) can be proved by the well-known circle criterion, the multivalued…
While periodic responses of periodically forced dissipative nonlinear mechanical systems are commonly observed in experiments and numerics, their existence can rarely be concluded in rigorous mathematical terms. This lack of a priori…
When a prediction algorithm serves a collection of users, disparities in prediction quality are likely to emerge. If users respond to accurate predictions by increasing engagement, inviting friends, or adopting trends, repeated learning…
Time crystals are a nonequilibrium phase of matter that extend fundamental spontaneous symmetry breaking into the temporal dimension, typically requiring external driving for their realization. Here, we explore the nonequilibrium phase…
The fast-slow dynamics of an eco-evolutionary system are studied, where we consider the feedback actions of environmental resources that are classified into those that are self-renewing and those externally supplied. We show although these…
We derive two fundamental trade-offs for general stochastic limit cycles in the weak-noise limit. The first is the dissipation-coherence trade-off, which was discovered and proved under additional assumptions by Santolin and Falasco [Phys.…
In repeated-game applications where both the collusive and non-collusive outcomes can be supported as equilibria, researchers must resolve underlying selection questions if theory will be used to understand counterfactual policies. One…